2021
DOI: 10.21468/scipostphys.10.4.093
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Charge quantization and detector resolution

Abstract: Charge quantization, or the absence thereof, is a central theme in quantum circuit theory, with dramatic consequences for the predicted circuit dynamics. Very recently, the question of whether or not charge should actually be described as quantized has enjoyed renewed widespread interest, with however seemingly contradictory propositions. Here, we intend to reconcile these different approaches, by arguing that ultimately, charge quantization is not an intrinsic system property, but instead depends on the spati… Show more

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Cited by 7 publications
(15 citation statements)
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References 59 publications
(145 reference statements)
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“…Moreover, in transport topological phase transitions [26][27][28][29][30][31][32][33][34][35][36][37], the compactness of the superconducting phase guarantees the conservation of topological charges [26] via the Nielsen-Ninomiya theorem [38]. This overall flurry prompted the proposition [39] that charge quantization depends ultimately on the spatial resolution with which charge is measured or interacted with (similar in spirit to a recent pedagogical review [40]), but that the spatial resolution is a basis choice and cannot change the size of the Hilbert space. In order to predict the correct number of available states in a circuit, it is therefore nonetheless relevant to have effective low-energy theories underpinned by a valid basis choice where the phase can be represented as compact.…”
Section: Introductionmentioning
confidence: 95%
“…Moreover, in transport topological phase transitions [26][27][28][29][30][31][32][33][34][35][36][37], the compactness of the superconducting phase guarantees the conservation of topological charges [26] via the Nielsen-Ninomiya theorem [38]. This overall flurry prompted the proposition [39] that charge quantization depends ultimately on the spatial resolution with which charge is measured or interacted with (similar in spirit to a recent pedagogical review [40]), but that the spatial resolution is a basis choice and cannot change the size of the Hilbert space. In order to predict the correct number of available states in a circuit, it is therefore nonetheless relevant to have effective low-energy theories underpinned by a valid basis choice where the phase can be represented as compact.…”
Section: Introductionmentioning
confidence: 95%
“…Similarly, the 8π-periodic Josephson en-ergy has four shifted copies (likewise within the same parity sector), cos([ϕ + 2πJ]/4) with J = {0, 1, 2, 3}, which can be associated to parafermionic edge states [52,53]. This feature of copied and shifted bands was argued to be generic and likewise rooted in CQ [38,59]. Physical realizations of topological superconductors are still underpinned by a condensate hosting an integer number of Cooper pairs (e.g., by proximitizing a topological material with a conventional s-wave superconductor).…”
mentioning
confidence: 97%
“…Moreover, in transport topological phase transitions [25][26][27][28][29][30][31][32][33][34][35][36], CQ guarantees the conservation of topological charges [25] via the Nielsen-Ninomiya theorem [37]. This overall flurry prompted the proposition [38] that CQ depends ultimately on the spatial resolution with which charge is measured, but that the charges of any circuit theory should always be quantizable, in the sense that there should always exist a basis choice with quantized charges.…”
mentioning
confidence: 99%
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